()) If \( \cos (\theta)=-\frac{8}{17} \) and \( 90^{\circ}<\theta<180^{\circ} \), what is \( \sin (\theta) \) ? \( \sin (\theta)= \) Write your answer in simplified, rationalized form.

To find \( \sin (\theta) \) given \( \cos (\theta) = -\frac{8}{17} \) and knowing that \( \theta \) is in the second quadrant (where sine is positive), we can use the identity \( \sin^2(\theta) + \cos^2(\theta) = 1 \). First, calculate \( \cos^2(\theta) \): \[ \cos^2(\theta) = \left(-\frac{8}{17}\right)^2 = \frac{64}{289} \] Now, use the Pythagorean identity: \[ \sin^2(\theta) + \frac{64}{289} = 1 \] Subtract \( \frac{64}{289} \) from both sides: \[ \sin^2(\theta) = 1 - \frac{64}{289} = \frac{289}{289} - \frac{64}{289} = \frac{225}{289} \] Next, take the square root of both sides. Since \( \theta \) is in the second quadrant, \( \sin(\theta) \) must be positive: \[ \sin(\theta) = \sqrt{\frac{225}{289}} = \frac{15}{17} \] Thus, the final answer is: \[ \sin(\theta) = \frac{15}{17} \]